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Nonlinear interferometer for Fourier-transform mid-infrared gas spectroscopy using near-infrared detection

Chiara Lindner, Jachin Kunz, Simon J. Herr, Sebastian Wolf, Jens Kießling, and Frank Kühnemann

Open Access Open Access

Abstract

Nonlinear interferometers allow for mid-infrared spectroscopy with near-infrared detection using correlated photons. Previous implementations have demonstrated a spectral resolution limited by spectrally selective detection. In our work, we demonstrate mid-infrared transmission spectroscopy in a nonlinear interferometer using single-pixel near-infrared detection and Fourier-transform analysis. A sub-wavenumber spectral resolution allows for rotational-line-resolving spectroscopy of gaseous samples in a spectral bandwidth of over 700 cm−1. We use methane transmission spectra around 3.3 μm wavelength to characterize the spectral resolution, noise limitations and transmission accuracy of our device. The combination of nonlinear interferometry and Fourier-transform analysis paves the way towards performant and efficient mid-infrared spectroscopy with near-infrared detection.

© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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Figures (7)
Fig. 1.
Fig. 1. (a) Setup of the nonlinear Michelson-interferometer. (b) Zoom into measured detector signals: reference pump interference (green) and signal interference (orange), modulated by movement of the idler mirror M$_{\textrm {i}}$. Every second zero-crossing (grey dots) of the pump interference signal is used as a reference for an equidistantly ($\lambda _{\textrm {p}}$) sampled interferogram.

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Fig. 2.
Fig. 2. Overview over the analysis procedure: (a) Steps in the treatment of the interferograms of reference and sample measurement. From the modulus (power spectral density) of the Fourier-transformed spectra, the non-apodized transmission spectrum can be calculated directly; alternatively, spectra using apodization can be calculated with the steps shown in (b).

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Fig. 3.
Fig. 3. Averaged interferogram of 100 reference measurement scans (light blue). The envelope of the interferogram results from dispersion of the nonlinear crystal. For apodization of the interferogram (steps shown in Fig. 2(b)), a reconstructed interferogram (dark blue) can be calculated by Fourier-transforming the power spectral density of the reference spectrum (Fig. 4).

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Fig. 4.
Fig. 4. Fourier-transformed spectra: Normalized power spectral density calculated by a Fourier-transform of the interferograms measured with pure nitrogen (reference, blue curve) and a mixture of 1 % methane in nitrogen (sample, orange curve). Both interferograms were averaged over 100 measurement scans.

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Fig. 5.
Fig. 5. Methane transmission spectrum calculated from the spectra shown in Fig. 4 without apodization (green) and using a Gaussian apodization function (red). The spectral ranges I-III highlighted in part (a) are further evaluated in section 4. Part (b) shows a detailed view of the absorption feature in spectral range III.

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Fig. 6.
Fig. 6. Detailed view of the measured transmission spectrum without apodization (green dots) and fitted model function (black curve). Parts (a) and (b) show the spectral ranges II and III highlighted in Fig. 5(a). The model function is based on a convolution of spectroscopic data and the sinc-shaped instrument function (Eqs. (7),(8)) and allows determining the maximum spectral resolution (${0.56}\;\textrm {cm}^{-1}$) of the measured data.

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Fig. 7.
Fig. 7. Measured transmission spectrum of methane using a Gaussian apodization function (red curve) which reduces the spectral resolution to about ${1}\;\textrm {cm}^{-1}$ (full width at half maximum). The black curve shows the model transmission function, based on a convolution of spectroscopic data and the Gaussian instrument function (Eq. (9)), which was fitted to the measured transmission data. The transmission residuum $\Delta T$ is shown in the lower graph (red curve).

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Equations (9)

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a ( x ) = exp ⁡ ( − ( x − L / 2 ) 2 2 ( α L ) 2 ) ,
SNR = μ σ .
P N = ϵ P h ν t F ,
S = η ϵ U ν ~ Δ ν ~ ,
U ν ~ = P ν ~ max − ν ~ min ,
SNR th = n S P N = η n t F ϵ P h ν Δ ν ~ ν ~ max − ν ~ min .
T m ( ν ~ ) = ( T th ∗ f ) ( ν ~ ) .
f ( ν ~ ) = 2 Δ ν ~ ⋅ sinc ( 2 π ν ~ Δ ν ~ ) ,
f ( ν ~ ) ≈ 1 2 π σ f exp ⁡ ( − ν ~ 2 2 σ f 2 ) ,
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